let p be non NAT -defined autonomic FinPartState of SCM ; :: thesis: for s1, s2 being State of SCM st p c= s1 & p c= s2 holds
for i being Element of NAT
for da, db being Data-Location
for I being Instruction of SCM st I = CurInstr (Computation s1,i) & I = Divide da,db & da in dom p & da <> db holds
((Computation s1,i) . da) div ((Computation s1,i) . db) = ((Computation s2,i) . da) div ((Computation s2,i) . db)
let s1, s2 be State of SCM ; :: thesis: ( p c= s1 & p c= s2 implies for i being Element of NAT
for da, db being Data-Location
for I being Instruction of SCM st I = CurInstr (Computation s1,i) & I = Divide da,db & da in dom p & da <> db holds
((Computation s1,i) . da) div ((Computation s1,i) . db) = ((Computation s2,i) . da) div ((Computation s2,i) . db) )
assume A1: ( p c= s1 & p c= s2 ) ; :: thesis: for i being Element of NAT
for da, db being Data-Location
for I being Instruction of SCM st I = CurInstr (Computation s1,i) & I = Divide da,db & da in dom p & da <> db holds
((Computation s1,i) . da) div ((Computation s1,i) . db) = ((Computation s2,i) . da) div ((Computation s2,i) . db)
let i be Element of NAT ; :: thesis: for da, db being Data-Location
for I being Instruction of SCM st I = CurInstr (Computation s1,i) & I = Divide da,db & da in dom p & da <> db holds
((Computation s1,i) . da) div ((Computation s1,i) . db) = ((Computation s2,i) . da) div ((Computation s2,i) . db)
let da, db be Data-Location ; :: thesis: for I being Instruction of SCM st I = CurInstr (Computation s1,i) & I = Divide da,db & da in dom p & da <> db holds
((Computation s1,i) . da) div ((Computation s1,i) . db) = ((Computation s2,i) . da) div ((Computation s2,i) . db)
let I be Instruction of SCM ; :: thesis: ( I = CurInstr (Computation s1,i) & I = Divide da,db & da in dom p & da <> db implies ((Computation s1,i) . da) div ((Computation s1,i) . db) = ((Computation s2,i) . da) div ((Computation s2,i) . db) )
assume A2: I = CurInstr (Computation s1,i) ; :: thesis: ( not I = Divide da,db or not da in dom p or not da <> db or ((Computation s1,i) . da) div ((Computation s1,i) . db) = ((Computation s2,i) . da) div ((Computation s2,i) . db) )
set Cs1i = Computation s1,i;
set Cs2i = Computation s2,i;
A3: I = CurInstr (Computation s2,i) by A1, A2, Th87;
set Cs1i1 = Computation s1,(i + 1);
set Cs2i1 = Computation s2,(i + 1);
A4: Computation s1,(i + 1) = Following (Computation s1,i) by AMI_1:14
.= Exec (CurInstr (Computation s1,i)),(Computation s1,i) ;
A5: Computation s2,(i + 1) = Following (Computation s2,i) by AMI_1:14
.= Exec (CurInstr (Computation s2,i)),(Computation s2,i) ;
A6: ( da in dom p implies ( ((Computation s1,(i + 1)) | (dom p)) . da = (Computation s1,(i + 1)) . da & ((Computation s2,(i + 1)) | (dom p)) . da = (Computation s2,(i + 1)) . da ) ) by FUNCT_1:72;
assume A7: ( I = Divide da,db & da in dom p & da <> db & ((Computation s1,i) . da) div ((Computation s1,i) . db) <> ((Computation s2,i) . da) div ((Computation s2,i) . db) ) ; :: thesis: contradiction
then ( (Computation s1,(i + 1)) . da = ((Computation s1,i) . da) div ((Computation s1,i) . db) & (Computation s2,(i + 1)) . da = ((Computation s2,i) . da) div ((Computation s2,i) . db) ) by A2, A3, A4, A5, AMI_3:12;
hence contradiction by A1, A6, A7, AMI_1:def 25; :: thesis: verum